Badspot is half right. Statistics show that 'more money' doesn't make a difference, but rather 'how you spend the money'
either way the less money you have the less money you have available to spend intelligently. if you have a school that's funded with billions of dollars and they funnel that into the sports program, the school will have really low achievement rates. if you fund that on art and science or math, then the achievement rates go up.
However, it doesn't matter because schools in poverty have less money to spend on those good aspects anyways